Reliability and Efficiency of DWR-Type A Posteriori Error Estimates with Smart Sensitivity Weight Recovering-Reference-Cited by-同舟云学术

Reliability and Efficiency of DWR-Type A Posteriori Error Estimates with Smart Sensitivity Weight Recovering

Published:2021-01-09 Issue:2 Volume:21 Page:351-371
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Endtmayer Bernhard¹^ORCID,Langer Ulrich²^ORCID,Wick Thomas³^ORCID

Affiliation:

1. Johannes Kepler University Linz , Doctoral Program on Computational Mathematics; and Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics, Altenbergerstr. 69, A-4040 Linz , Austria

2. Austrian Academy of Sciences , Johann Radon Institute for Computational and Applied Mathematics , Altenbergerstr. 69, A-4040 Linz , Austria

3. Institute of Applied Mathematics , Leibniz University Hannover , Welfengarten 1, 30167 Hannover , Germany

Abstract

Abstract We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [B. Endtmayer, U. Langer and T. Wick, Two-side a posteriori error estimates for the dual-weighted residual method, SIAM J. Sci. Comput. 42 2020, 1, A371–A394], we showed efficiency and reliability for error estimators based on enriched finite element spaces. However, the solution of problems on an enriched finite element space is expensive. In the literature, it is well known that one can use some higher-order interpolation to overcome this bottleneck. Using a saturation assumption, we extend the proofs of efficiency and reliability to such higher-order interpolations. The results can be used to create a new family of algorithms, where one of them is tested on three numerical examples (Poisson problem, p-Laplace equation, Navier–Stokes benchmark), and is compared to our previous algorithm.

Funder

Austrian Science Fund

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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